Techniques for Approximating Optimal Linear Estimators of Multidimensional Data
Atkinson, Ian Charles
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https://hdl.handle.net/2142/81052
Description
Title
Techniques for Approximating Optimal Linear Estimators of Multidimensional Data
Author(s)
Atkinson, Ian Charles
Issue Date
2007
Doctoral Committee Chair(s)
Kamalabadi, Farzad
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
This framework is used to create estimators for four distinct applications. First, we create a blind estimator for hyperspectral and multispectral data that improves the average channel signal-to-noise ratio of a 0 dB observation by 16 dB. Second, we consider the problem of estimating a time-series of optical coherence tomography images and propose a blind estimator that improves visual image quality by reducing the speckle noise that is characteristic of coherent imaging. Next, a blind estimator for fMRI data is constructed that significantly improves the ability to detect low CNR functional activation in small regions of activation without a compromise to the false detection rate. Finally, the concepts developed for the multidimensional estimation framework are used to illustrate how regularized reconstruction of noisy projection data can be improved by exploiting the angular correlation of the true data. In the setting of a filtered back-projection (FBP) reconstruction scheme, this corresponds to performing the filtering step of the well known FBP method in a non-Radon domain. Doing so greatly improves the reconstruction quality of highly noisy projection data.
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